SOLUTION: PROVE ALGEBRAICALLY THAT: ( (xy) / (1+(xz)) ) > ( ((xy)+(ab)) / (1 + (xz) + (ac)) ) REDUCES TO: (b/c) < ( (xy) / (1+(xz)) ). I HAVE NO IDEA WHERE TO EVEN START!!

Question 32245: PROVE ALGEBRAICALLY THAT: ( (xy) / (1+(xz)) ) > ( ((xy)+(ab)) / (1 + (xz) + (ac)) ) REDUCES TO: (b/c) < ( (xy) / (1+(xz)) ).
I HAVE NO IDEA WHERE TO EVEN START!!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
PROVE ALGEBRAICALLY THAT: ( (xy) / (1+(xz)) ) > ( ((xy)+(ab)) / (1 + (xz) + (ac)) ) REDUCES TO: (b/c) < ( (xy) / (1+(xz)) ).
I HAVE NO IDEA WHERE TO EVEN START!!
DONT GET SCARED!KEEP UP THE SPIRIT.WE SHOULD LEARN HOWTO REMOVE THE VEILS OR CAMOUFLAGE TO LOOK AT THE REAL FRUIT.
FOR THIS PURPOSE WE USE ONION PEEL APPROACH...REMOVE THE OUTR LAYERS ONE BY ONE...AND BUILDING BLOCKS..WE TRY TO LEARN FROM SMALL THINGS TO BIG THINGS.
HERE THERE ARE BIG EXPRESSIONS..LET US SIMPLIFY BY NEW SYMBOLS.
LET US CALL L= ( (xy) / (1+(xz)) )......AND M = ( ((xy)+(ab)) / (1 + (xz) + (ac))
AND K = (b/c).....HENCE GIVEN L > M , TST.....K < L..........
LET US STUDY SOME EXAMPLES...SUPPOSE
IF L=4/2=NUMBER GREATER THAN 1...THEN YOU CAN EASILY SEE THAT ADDING SAME NUMBER...SAY 2 TO NR AND DR WILL MAKE THE NEW NUMBER (4+2)/(2+2)=6/4=3/2 SMALLER.

IF L=4/2=NUMBER GREATER THAN 1...THEN YOU CAN EASILY SEE THAT SUBTRACTINGING SAME NUMBER...SAY 1 FROM NR AND DR WILL MAKE THE NEW NUMBER (4-1)/(2-1)=3/1=3 BIGGER.
IF L=2/4=NUMBER SMALLER THAN 1...THEN YOU CAN EASILY SEE THAT ADDING SAME NUMBER...SAY 2 TO NR AND DR WILL MAKE THE NEW NUMBER (2+2)/(4+2)=4/6=2/3 BIGGER.
IF L=2/4=NUMBER SMALLER THAN 1...THEN YOU CAN EASILY SEE THAT SUBTRACTING SAME NUMBER...SAY 1 FROM NR AND DR WILL MAKE THE NEW NUMBER (2-1)/(4-1)=1/3= SMALLER.
THIS IS FUNDAMENTAL PROPERTY OF FRACTIONS.
NOW WE HAVE
K=B/C..OR..B=KC....SO AB =KAC
WE ARE GIVEN THAT
L>(L+KAC)/(1+AC).....FROM THIS AND ABOVE PROPERTIES OF FRACTIONS,WE SEE THAT
IF L >1...THEN AC IS POSITIVE...AND IF L< 1 THEN AC IS NEGATIVE.
I SHALL SHOW YOU THE PROOF FOR THE FIRST ALTERNATIVE AND YOU CAN DO FOR THE SECOND ALTERNATIVE.
L >1 AND AC IS POSITIVE
L-(L+KAC)/(1+AC)>0
(L+LAC-L-KAC)/(1+AC)>0
AC(L-K)>0...SINCE AC IS POSITIVE AND HENCE 1+AC IS POSITIVE.
L-K>0........SINCE AC IS POSITIVE
L>K...OR K
RELATED QUESTIONS
Given: XZ=YW Prove:... (answered by greenestamps)

xy = 11 xz = 4c xz = 83 solve for... (answered by edjones)

If XY=ZY, XZ=4x + 1, and ZY= 6x -13, prove that x=7. Use proper proof notation. (answered by Fombitz,MathTherapy)

Factorize... (answered by MathLover1,Edwin McCravy,math_helper)

If x+y+z=1 and x^2+y^2+z^2=3 then find the value of xy+xz+yz. I really don't know where... (answered by palanisamy)

is xz+xy = xz+yz and xz+xy = xy + xz both using the commutative property of... (answered by stanbon)

I need help with this proof. Given: triangle WOZ is congruent to triangle WOY Prove: XY (answered by Alan3354)

xy+xz=2 yx+yz=2... (answered by aaaaaaaa)

I have to solve this problem by multiplying and then simplying: (square root of... (answered by checkley77)